Title: Probing the connections between superconductivity, stripe order, and structure in La₁.₉₀₅Ba₀.₀₉₅Cu1-yZnyO₄

The superconducting system La2-xBaxCuO₄ is known to show a minimum in the transition temperature Tc at x=1/8 where maximal stripe order is pinned by the anisotropy within the CuO₂ planes that occurs in the low-temperature-tetragonal (LTT) crystal structure. For x=0.095, where Tc reaches its maximum value of 32 K, there is a roughly coincident structural transition to a phase that is very close to LTT. Here, we present a neutron scattering study of the structural transition, and demonstrate how features of it correlate with anomalies in the magnetic susceptibility, electrical resistivity, thermal conductivity, and thermoelectric power. We also present measurements on a crystal with 1% Zn substituted for Cu, which reduces Tc to 17 K, enhances the spin stripe order, but has much less effect on the structural transition. We make the case that the structural transition correlates with a reduction of the Josephson coupling between the CuO₂ layers, which interrupts the growth of the superconducting order. We also discuss evidence for two-dimensional superconducting fluctuations in the normal state, analyze the effective magnetic moment per Zn impurity, and consider the significance of the anomalous thermopower often reported in the stripe-ordered phase.